Many parametric measurements are subject to different types of noise. The sources of the noise could be from the signal or circuit under test, or from the measurement instrument. Averaging has been used to increase the measurement precision and repeatability for static parameters. Examples of such parameters include DC voltage or current, clock period, signal skew, or device propagation delay.
Typically, when an average quantity is to be measured, a number of samples are taken within the data acquisition window and the results averaged. If the noise frequency is larger than the inverse of the averaging window, the standard deviation of the average quantity from one measurement to the next will reduce as below:
                              s          _                =                                                            1                N                            ⁢                                                ∑                                      =                                                                                  ⁢                                          i                      ⁢                                                                                          ⁢                      1                                                        N                                ⁢                                                                  ⁢                                  s                  i                                                      →                          σ                              s                _                                              =                                    1                              N                                      ⁢                          σ              s                                                          Equation        ⁢                                  ⁢        1            where si are the individual samples of the parameter to be measured, N is the number of samples, s is the average over N samples, and σX denotes the standard deviation of parameter X.
FIG. 1 illustrates an exemplary frequency response of an averaging process. As evident from FIG. 1, the averaging process is effective for reducing noise or jitter at frequencies greater than 1/10th of the inverse of the averaging window. This means that the lower frequency noise can result in measurement error, especially if the low frequency noise power is substantial. Examples of such noises include 1/f flicker noise in CMOS devices and 1/f2 phase noise in oscillators.
One solution for reducing the impact of low frequency noise is to use a longer averaging window. This, however, has the disadvantages of increased measurement time and reduced effectiveness if the low frequency noise power spectrum has 1/fn (n≧1) characteristics.
While various methodologies for compensating for low frequency jitter have been developed, no design has emerged that generally encompasses all of the desired characteristics as hereafter presented in accordance with the subject technology.